Correct

立刻 vs 立即

/ lìkè vs lìjí /
Strokes

Definition

立刻 and 立即 both are Adverbs, witch means [at once; immediately].

Example

立刻 indicates that an action or situation is to appear very soon or that an action or situation appears closely after another action or situation with the stress on the shortness of time.
1) 立刻 is more colloquial. Example ② is a colloquial sentence, so 立刻 and not 立即 is used.

2) In examples, ① ③ and ④ 立即 can also be used instead.

3) If 立即 is used in the example, 开始 may be omitted.
1
jiā
大家
立刻
集合
  

Please gather at once.

2
Tiān
tài
le
  
,
dòng
dòng
一动
立刻
jiù
mǎnshēn
满身
hán
  

It's so hot that we will sweat all over as soon as we take a move.

3
Shōudào
收到
men
他们
de
xìn
hòu
  
,
立刻
xiě
le
huíxìn
回信
  

I replied as soon as I heard from them.

4
àn
diànniǔ
电钮
  
,
机器
立刻
kāishǐ
开始
yùnzhuǎn
运转
  

The machine started the moment he pressed the button.

立即 means "the instant when, at the very moment of speaking", with the stress on no intermission. It is used mostly in written language.
In examples, ⑤ ⑥ ⑦ 立刻 can be used instead but it would be more colloquial.
5
Tīngdào
听到
jiào
呼叫
  
,
立即
  
(
立刻
  
)
pǎo
xià
lóu
  

He ran downstairs immediately he heard the call.

6
jiā
大家
立即
  
(
立刻
  
)
xíngdòng
行动
lai
起来
  
,
yào
不要
dānge
耽搁
shíjiān
时间
  

Please take action at once.Don't delay.

7
Jiēdào
接到
diànhuà
电话
  
,
立即
  
(
立刻
  
)
gǎndào
赶到
le
chūshì
出事
xiànchǎng
现场
  

I hurried to the accident spot as soon as I received the phone.